The offer came shortly after Japanese investment giant SoftBank secured its own stake in the ride-sharing company in January, according to Bloomberg, which cited anonymous sources.

Uber and Berkshire Hathaway disagreed on the terms and size of the deal, according to the report, so Uber tried to talk Buffett into a smaller stake.

"One of my business goals in life has been to get Warren Buffett to invest in something that I'm involved in and, so far, I failed," Khosrowshahi told CNBC's Carl Quintanilla in an interview late Wednesday.

Khosrowshahi said it's possible the parties could revisit a deal in the future, but that Uber's "enormous growth trajectory" comes with "considerable risk."

"I don't think we necessarily fit in with the typical Warren Buffett investment. Maybe we can be a different kind of an investment, a portfolio diversification play for him," he said.

The company has been in the middle of a reputational turnaround since its controversial founder Travis Kalanick was ousted last year. Khosrowshahi has emphasized rider safety, driver rights and better governmental relations in his 10 months as CEO.